Suppose that the demand function for a certain product isq = 400 - 4p(a) Enter the equation for revenue R as a function of price p(b) What is the (instantaneous) rate of change of revenue with respect to price when the price is $ 14?(c) At what price is the derivative of revenue with respect to price exactly zero?

Question
Asked Feb 18, 2019

Suppose that the demand function for a certain product is
q = 400 - 4p

(a) Enter the equation for revenue R as a function of price p

(b) What is the (instantaneous) rate of change of revenue with respect to price when the price is $ 14?

(c) At what price is the derivative of revenue with respect to price exactly zero?

check_circleExpert Solution
Step 1

Given:

The demand function is q = 400-4p.

Step 2

(a)

Obtain the revenue function.

Calculation:

 In general the revenue function is represented in the form of R = pq, where p is the price per item and q is the demand function.

Thus, the revenue function for the given demand function is R = p(400−4p).

Thus, the revenue function is R = 400p−4p2.

Step 3

(b)

Calculate the rate of change of revenue with respect to the price when the price is $14.

Calculation:

 Derivate ...

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